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Solvable groups with restrictions on Sylow subgroups of the Fitting subgroup

Alexander Trofimuk

Department of Mathematics, Brest State University named after A. S. Pushkin, 21, Boulevard of Cosmonauts Brest, Belarus

E-mail Address: alexander.trofimuk@gmail.com

https://doi.org/10.1142/S1793557116500376Cited by:1 (Source: Crossref)

Abstract

In this paper, we study solvable groups in which $r_{n} (F)$ is at most 2. In particular, we investigated groups of odd order and $A_{4}$ -free groups with this property. Exact estimations of the derived length and nilpotent length of such groups are obtained.

Communicated by A. F. Vasil’ev

Keywords:

AMSC: 20D10

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